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CanadaON
Grade 11

Single transformations of sine and cosine

Interactive practice questions

Consider the two graphs:

$A$A: $y=\sin x$y=sinx

$B$B: $y=\sin x+3$y=sinx+3

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What vertical shift of $y=\sin x$y=sinx results in the graph of $y=\sin x+3$y=sinx+3?

Translating the graph $4$4 units upwards.

A

Translating the graph $4$4 units downwards.

B

Translating the graph $3$3 units downwards.

C

Translating the graph $3$3 units upwards.

D
Easy
< 1min

Consider the two graphs:

$A$A: $y=\cos x$y=cosx

$B$B: $y=\cos x+4$y=cosx+4

Easy
< 1min

Consider the function $y=\sin x+2$y=sinx+2.

Easy
3min

Consider the function $y=\cos x+2$y=cosx+2.

Easy
2min
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Outcomes

11U.D.2.5

Determine, through investigation using technology, the roles of the parameters a, k, d, and c in functions of the form y =af (k(x – d)) + c, where f(x) =sinx or f(x) =cosx with angles expressed in degrees, and describe these roles in terms of transformations on the graphs of f(x) =sinx and f(x) =cosx

11U.D.2.6

Determine the amplitude, period, phase shift, domain, and range of sinusoidal functions whose equations are given in the form f(x) = asin(k(x – d)) + c or f(x) = acos(k(x – d)) + c

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